**Homomorphisms and Isomorphisms**

A *homomorphism* between two Boolean algebras *A* and *B* is a function *f* : *A* → *B* such that for all *a*, *b* in *A*:

*f*(*a*∨*b*) =*f*(*a*) ∨*f*(*b*),*f*(*a*∧*b*) =*f*(*a*) ∧*f*(*b*),- f(0) = 0,
- f(1) = 1.

It then follows that *f*(¬*a*) = ¬*f*(*a*) for all *a* in *A* as well. The class of all Boolean algebras, together with this notion of morphism, forms a full subcategory of the category of lattices.

Read more about this topic: Boolean Algebra (structure)